It depends on how the index is constructed. A market cap index cannot be value investing. A market sector index is almost surely not value investing (unless that entire sector is undervalued).

An index constructed specifically using value measures as the criteria for inclusion can be (at least arguably so).

Click on "value indexes" here: https://www.crsp.org/indexes/ to see some underlying value indexes, and funds like this one track the Large Cap version of it: https://fundresearch.fidelity.com/mutual-funds/summary/92290... (perhaps not surprising, the fund's largest holding is Berkshire B shares)